Step 1: Get What You Need:
-A Clip from a dog leash. Dollar Tree, at least in my area, sells dog leashes for a dollar. They have rectangular loops with swivel ends to prevent tangling. The rectangular loops are able to fit around a strap without a keyring. However, you should check the loop size because they had regular ones and small ones, and I bought the small one which is too small for the loop. However, it was only a dollar, so I can get the right one tomorrow.
-A Keyring- These are only necessary if the strap is too wide to fit a standard leash clip around it (or if you didn't measure and got a small one). A good, large keyring is pretty strong, surely strong enough to carry the average size camera/lens. My NEX-5n weighs less than a pound, so I am confident carrying it on it. Do not get the swing open ones. That is an accident waiting to happen.
-String/Something to attach the camera to the hook. I used Hemp string because it is thin and I had a bunch lying around. I attached it to the strap hooks on my camera, so it needed to be thin enough to be braided and still fit.
Step 2: Optional:Put the Ring on the Dog Leash Loop.
Take the keyring and hook it to the square part of the leash
Step 3: Put the Main Part Together
Put the ring over one end so it is on the strap.
Close the loop by slipping the strap through and closing it. Now the loop is stuck on the strap.
The main piece is done.
Step 4: Make Something to Attach the Camera to the Hook.
I had some hemp string randomly lying on my desk. It just so happens that when braided in a classic 3 strand braid( ||| put left over middle X| Then put right over new middle |X Repeat etc.) made it thin enough and more than strong enough to hold the camera while still fitting through the strap eyelet. Braid about 4in worth.
For mine, because I like it short, there is only ~2in of the braid in use (Circumfrence of loop is 2in.). Make a loop knot and trim the ends. Slip it through the camera, and poke the knot through bit of string that is poking out. Pull it all shut like in the picture so it doesn't slip off.
Step 5: You're Done!
EDIT: I attached a GIF, so click on it and you can see it in action.